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" BG; and things that are equal to the same are equal to one another; therefore the straight line AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the given straight line BC. "
Elements of Geometry: Containing the First Six Books of Euclid, with a ... - Side 19
av Euclid, John Playfair - 1826 - 320 sider
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864
...the remainder BG ; (ax. 3.) but it has been shewn that BCis equal to BG, wherefore AL and .BCare each of them equal to BG; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore...
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Works, Volum 8

Francis Bacon - 1864
...whereas in distributive, if unequals be not given to unequals there is the greatest injustice.1 Again " things that are equal to the same are equal to one another," is likewise a rule of mathematics ; but it is at the same time so potent in logic as to be the basis...
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The college Euclid: comprising the first six and the parts of the eleventh ...

Euclides - 1865
...the same thing are equal to one another ; therefore tne straight line AI. is equal to BC. (ax. 1.) Wherefore from the given point A a straight line AL...has been drawn equal to the given straight line BC. Which was to be done. PROP. III.— PROBLEM. From the greater of two given straight lines to cut off...
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Philosophy of Sir William Hamilton, Bart: Professor of Logic and Metaphysics ...

Sir William Hamilton - 1866 - 530 sider
...certainly than through demonstration, that we know in a common notion.' .... Such common notions are—' Things that are equal to the same are equal to one another,'—' If equals be taken from equals the remainders are equal,'—' Every thing must be either affirmed or...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 sider
...to BG. But things which are equal to the same thing are equal to one another. [Axiom 1 . Therefore AL is equal to BC. "Wherefore from, the given point...has been drawn equal to the given straight line BC. QEF PROPOSITION 3. PROBLEM. From the greater of two given straight lines to cut off a part equal to...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 sider
...equal to BG. But things which are equal to the same thing are equal to one another. [Axiom 1. Therefore AL is equal to BC. Wherefore from the given point A a straight line AI, has been drawn equal to the given straight line BC. QEP PROPOSITION 3. PROBLEM. From the greater...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 sider
...the remainder BG; (ax. 3.) but it has been shewn that .BCis equal to BG, wherefore AL and BCaie each of them equal to BG; and things that are equal to the same thing are equal to one another ; therefore the straight line AL is equal to BC. (ax. 1.) Wherefore...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - 1872
...straight line, the adjacent £s so formed are together equal to two right £s. (Prop. XIII.) 2. That things that are equal to the same are equal to one another. (Ax. I.) 3. That if the same quantity be taken from two equal quantities the remainders are equal....
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873
...equal to the remainder BG; but it has been shown that BC is equal to BG ; wherefore AL and BC are cash of them equal to BG ; and things that are equal to the same are equal to one another ; therefore AL is equal to BC. Wherefore from the given point A a straight line AL has been drawn equal to the...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...to BG ; and things which are equal to the same thing are equal to one another (Ax. 1) ; therefore 4. The straight line AL is equal to BC. Wherefore, from...has been drawn equal to the given straight line BC. Which was to be done. PROPOSITION 3. — Problem. From the greater of two given straight lines to cut...
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